In tire building machines of the type seen in Cantarruti U.S. Pat. No. 3,438,832, Enders U.S. Pat. Nos. 3,728,194 and 4,302,274, or as sold by NRM Corporation of Akron, Ohio under the well-known Model Nos. 88C and 88D, dual bladders are employed at each end of a tire building drum to wrap the plys of the tire carcass around a bead which has been set against the turned-down plys at the end of the drum. A dual bladder assembly in the more conventional beaded bladder type which may comprise five or more clamping or air supply rings must normally be disassembled, replaced, and reassembled if the machine is to be converted from the manufacture of one size tire to another. This not only requires a substantial amount of disassembly and assembly time, but also requires the tire manufacturer to maintain a significant inventory of costly clamping and air supply rings for each size tire.